# trigonometry's questions - English 1answer

280 trigonometry questions.

### 13 Factorize trigonometric matrices

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions: M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...

### 1 Strange output for solve in terms of trigonometric functions

1 answers, 35 views equation-solving trigonometry
I am using the following Solve code: ...

### 5 Feature of quaternion Cos, Cot etc

1 answers, 153 views trigonometry quaternions
I am new to SE Mathematica, and search gives no answer; so here is my problem: During the testing of my numerical library for quaternions with Mathematica (package Quaternions) I observed the ...

### 3 Inconsistent results for symbolic trigonometric integral

0 answers, 141 views calculus-and-analysis trigonometry
I am trying to evaluate (on Mathematica v.9) the integral $$\int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y,$$ where $t$ is an even, positive integer. ...

### Defined function doesn't plot correctly

I have defined a function that produces a single negative impulse spanning -b to -a and a positive impulse spanning ...

### 6 Integral that yields ArcTan function rather than ArcSin

1 answers, 234 views calculus-and-analysis trigonometry
When I enter the following Integral problem to Mathematica, $$\int \frac{1}{\sqrt{a²-x²}}\textrm{d}x$$ The answer yielded by Mathematica is $$\arctan\left({\frac{x}{\sqrt{a²-x^2}}}\right)$$ Rather ...

### 1 Plot of integral of summed Sinc series is incorrect

I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy: ...

### 9 Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

7 answers, 2.319 views calculus-and-analysis trigonometry proof
As an intermediate step, consider the function:f[x_] := x Sin[Pi/x]I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...

### Incorrect results in trig table

I have a table given byTable[ Evaluate[ Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]], {r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0The ...

### 1 Find closed form for roots of trig formula

I have the expressionSum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0I want to find the roots in terms of ...

### 3 Symbol Order for Built-in Functions such as TrigReduce

1 answers, 106 views symbolic trigonometry order
I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order ...

### 3 Indefinite ArcTan integral does not return the (known) real expression but returns complex expression

2 answers, 83 views calculus-and-analysis trigonometry
I have a problem with an indefinite integral which I solved using MMA in back in 2010 (must have been version 7 or 8) successfullly and it gave an elegant result. However, if I run it with MMA 11.3 (...

### 3 Indeterminate result from Sinc

1 answers, 116 views error fourier-analysis trigonometry
I have an impulse train given by(1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R)Because of the Csc, ...

### 4 Solve/Reduce not working on a function with a condition/domain restriction?

I'm working with a trigonometric function, so I thought it would be convenient to set a condition to restrict the domain so I wouldn't have to specify it in the solve function each time. Here is a ...

### 3 Prevent Trigonometric simplifications from using double angle and half angle formulae?

Is there any way to force Mathematica to not use double and half angle formulae etc. when simplifying Trigonometric expressions? For example,...

### 2 Convert trigonometric expression into other forms using just a specific set of identities

I am trying to convert a trigonometric expression likesinθ/(1 - cosθ)intocosecθ + cotθor ...

### 2 Solve simple trig equation

5 answers, 4.323 views equation-solving trigonometry
I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to <...

### 1 Why is this function indeterminate?

1 answers, 58 views error series-expansion trigonometry
Consider an impulse train1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For x=0 it's clear that this function ...

### How can I avoid the message Infinity::indet?

2 answers, 94 views error series-expansion trigonometry
I have an impulse train of frequency R:1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For ...

### Force a result from “Indeterminate” for single impulse?

The formula for a single impulse of amplitude $1$ at $x=r$ is given by $$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$ (In MathJax because it's a math formula.) Formally, at $x=r$, this function evaluates ...

### 1 Trigonometric simplification with assumptions fails

Consider the following inputAssuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...

### 2 Simplification of a product of trigonometric functions

3 answers, 132 views simplifying-expressions trigonometry
I have this expression2 Csc[2 y[x2]] Sech[x[x2]]^2 (Cos[y[x2]]^4 Cosh[x[x2]]^8 Sin[y[x2]]^4)^(1/4)which is 1. But Mathematica doesn't do the simplification. I ...

### Get the square root of a+bi,when a>0,b>0 in radical form

My code returns this result involves trigonometric functions, ...

### Plotting a function while varying a variable (on the x-axis) using two formulas [duplicate]

I want to plot the following function, where Rb is the variable (that has to be on the x-axis): ...

### 1 Not getting expected simplification of trigonometric expressions

1 answers, 40 views trigonometry
I have two trigonometric expressions. I would like to eliminate the fraction from my 2nd expression. ...

### 1 Solve trig equation

2 answers, 62 views equation-solving trigonometry homework
I have a simple trig equation:Clear[f, x] f[x_] = Cos[2*x] - 3 Sin[x] + 2 Solve[f[x] == 0, x]I received a very long a complicated reply that I do not ...

### Plotting a function that has variables out of an other piece of code

I've the following code: ...

...

### 1 Substitution in trigonometric expressions to remove secant and cosecant functions

1 answers, 82 views replacement trigonometry
I manipulate equations which are trigonometric equations in mechanics. In theses equations, the custom is to use only Cos, Sin and Tan functions and not the secant and cosecant functions. To prevent ...

### Trig function graphing exercise [closed]

2 answers, 86 views plotting trigonometry homework
I am trying to figure out how to do the following exercise in Mathematica Graph $y(t)= a \cos t + b \sin t - 0.5 \sin t$ on the interval $0 ≤ t ≤ 6\, π$

### Verify solution of system of first order ODE

I am given a solution $v_1$(t)=$-e^{t/2}cost$ for a system of first order ODE and I am asked to verify this solution can solves the linear second order ODE in terms of $y_1$(t) Here is the matrix ...

### Solving a trig equation in a specific range

I want to define a function as suchg[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]]However the result comes out as a conditional expression, for ...

### How to get a single evaluation of RandomReal in a Block

I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]). The two ...

### User defined ArcTan function

I am trying to integrate an equation that requires an angle term calculated using ArcTan[x,y]. A number of issues have been mentioned about ...

### 4 How to solve this trigonometric system of equations numerically?

1 answers, 363 views equation-solving numerics trigonometry
How can the following trigonometric system of equations be solved numerically? ...

### 1 “Power series” in Cos[n*x] for X coordinate of planetary ellipse

1 answers, 124 views fitting trigonometry
Consider the functions below: ...

### 1 I want to graph all of ArcSin without restriction, how would I format that? [closed]

2 answers, 118 views plotting trigonometry
I am new to this and I've plotted this:Plot[3 ArcSin[x + 4] - 16, but I don't know what/how to specify the range?

### 38 How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I triedSolve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]It returns the ...

### 2 Axes labels as multiples of $\pi$

3 answers, 2.727 views plotting labeling trigonometry
I have a list as containing seven elements: ...

### 1 Determining the angle x through the point of intersection between lines in any triangle [closed]

0 answers, 55 views trigonometry
I'm trying to determine the angle x in the triangle shown below. Given $\overline{DB}=\overline{DE}$ Given $\overline{AD}=\overline{DC}$ Given $\angle ADE=40^°$ Find $\angle DCB$ But I'm finding ...

### 7 Quantity and Trig functions

1 answers, 276 views trigonometry version-9 units
I have a bunch of data to which I've assigned units using Quantity, including some angular measurements in degrees. I'd like to be able to use these measurements ...

### 2 To solve this problem just follow this rule or is there another possibility?

5 answers, 152 views equation-solving trigonometry
To solve this problem just follow this rule or is there another possibility?Solve[(3 Sqrt[2])/Sin[60 Degree] == x/Sin[45 Degree], {x}]

### 1 Different solutions for $\sin (2x)-\cos (2x)= 1$ and $\sin(2x) = 1 + \cos(2x)$ [closed]

I am trying to solve an equation in Wolfram Mathematica and I get different results although the equation is technically the same. I am really confused. so basically: $\sin(2x) - \cos(2x)= 1$ is the ...

### 1 Equivalence of ComplexExpand and assuming real arguments

I am wondering why this simplification does not work,FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]] (*Out[1]= Im(csc(a))*)while this does:<...

### 1 Differential equation, Inverse Functions being used and a way to bypass it.

0 answers, 54 views differential-equations trigonometry
I have the following differential equation ...

### 1 How can Mathematica simplify this trigonometric function?

2 answers, 132 views simplifying-expressions trigonometry
This question must be too simple, but it confused me for several days. I want to know how can I do the following simplification using Mathematica: For example, convert ...

### 2 Error of InverseFunction

Update This bug has been fixed in v11.3.0. And as @Carl Woll has pointed out, the imaginary part of Sin and negative sign of Cos...

### 26 Extract real part of a complex expression better than Re does

1 answers, 23.144 views symbolic trigonometry
I have a complex expression with real positive variables only. Mathematica Input Style: ...

### 4 ArcTan apply to nested list

5 answers, 276 views list-manipulation trigonometry
I have a coordinate system generated by :coord = Table[{x, y}, {x, 5}, {y, 5}]I would like to calculate ArcTan(y/x) and ...

### 3 How to find non-overlapping triangles?

There are at least a few non-overlapping triangles made by the lines in the following graphic, how would I isolate them? ...